WATER RESOURCES RESEARCH, VOL. 29, NO. 2, PAGES 515-520, FEBRUARY 1993 Application of Energy Concepts to Groundwater Flow: Adaptive Modelingof a Leaky Aquifer ASITHA SENEVIRATNE 1 AND BRYAN KARNEY Department of Civil Engineering, University of Toronto, Toronto,Ontario, Canada The net work and energyflux at the boundaries of an aquifer change its internal energyand overcome its resistance to flow. In saturated porous media, the change in internal (strain) energy is stored in the elasticsoil matrix andin pore water compression. In unsaturated media, an additional term accounts for changes in gravitational potential energy. The energy approach complements conventional insight by allowing spatially distributed processes to be integrated into energy and work termswhich characterize a system's response to a set of excitations. Specifically, a technique is developed in thispaper to interpret thedynamic behavior of a one-dimensional leaky aquifer in terms of its composite energy functions. In particular, the work interaction at the leaky boundary is used as an index of the significance of the leakage: when the work parameter indicates a relatively small leakage,the flow components of the multiaquifer can be isolated and modeled separately with a controllable loss of accuracy. INTRODUCTION Transient flow conditions in a porous medium can be described in terms of composite energy functions. The underlying concept is that disturbances in equilibriumflow conditions--whether brought about by work at a system's boundaries, by heat exchange, or by direct matter/energy transfer--are associated with changesin a system's energy. Shifts in the relative magnitude of the various energynorms thus indicate the dominance of the different physical phe- nomena in the system as well as the importance of phenom- ena at its boundaries. Unlike the traditional approach of calculating the flow velocity and piezometric headat a point or a set of points, the energy method directly provides an integratedview of the transient response of the entire system. In a previous paper, Karney and Seneviratne [1991] ap- pliedthe energy conceptto assess transientconditions in confined aquifers. In particular, therateof change of internal energy of the porousmediumwas shown to be a natural index of the unsteadiness of the system, an insight which led to an adaptive algorithmfor adjusting the time step in a transient flow model. In addition, the energy principle was used to compute the sensitivity of different aquifer regions to dataacquisitionerrors. In thecurrent paper, energy expressions arepresented for bothconfined and unconfined aquifers and their work inter- action through a leaky boundary. As subsequent develop- mentsshow, the rate work is done at a leaky boundary provides a robustindicationof the significance of the leak- age. In fact, when the work acrossthe leaky boundary is relatively small, the leaky system can be replacedby a simpler confined flowmodel, subject to a controllable loss of accuracy. Thisis important, for the assumption thatconfin- ing formations areimpervious is seldom satisfied. Because of subsurface irregularities, confinements tend to vary from less to highly pervious, thuscausing complex groundwater 1Now at Bechtel Corporation, San Francisco, California. Copyright 1993 by the American Geophysical Union. Paper number 92WR02449. 0043-1397/93/92 WR-02449502.00 flow patterns. Hence the importance of leakage between adjacent aquifers/aquitards forms a continuumof flow inter- actions, ranging from strongto weak, for which the tradi- tional designations of "confined" and "leaky" are special cases.It has been typical in groundwater modeling to treat leaky and confinedcasesas discrete options rather than as a continuum of approximations. In modeling groundwater flow, "leakage" strictlyrefersto flow interactions whichtake place through top and/orbottom confining layers. Yet such systemsoften consistof three or more individual flow components.For example, a confined aquifer overlain by an unconfinedaquifer could have an intervening silt layer which is semipervious causing a flow interaction. Only rarely can the dynamic response of one component in such a multiaquifer be isolated from another a priori. Usually, the systemneeds to be modeled simulta- neously, which requires both extensive computational effort and considerable hydrogeologic data, particularly under transient conditions.However, if a procedure can be found which demonstrates that the flow interactions between the two aquifers is indeed negligible, then it may be possible to analyze eachcomponent separately, thus reducing data and computational time requirements. The energyapproach presented in this paper providesa basis for switching from a leaky model to a confined model by calculating the work term at the leaky boundary.The importance of the leakage is evaluated on the relative magnitude of the flow work occurring during the period of simulation. Specifically, the relative magnitude of the leak- age istaken astheratioof the magnitude of the work done at theleakyboundary at any giventime to the magnitude of the maximum work done at that boundary during the period of simulation. When the work interaction at the leaky boundary is less than a user-specified threshold value, the model switches from the leaky to a confined model. In order to place these developments in perspective, a brief reviewof the flow equations and energy relations is first presented. SIMPLIFIED MULTIAQUIFERFLOW EQUATIONS The present study considers a relatively simple two- aquifer system--aconfined aquiferoverlainby an uncon- 515